An earlier GOP measure to raise the debt ceiling included a host of GOP priorities, including defunding ObamaCare and constructing the Keystone XL pipeline, but not dollar-for-dollar spending cuts.

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Now, as it looks increasingly like the government shutdown fight will be paired with raising the debt ceiling, Republicans are pushing hard for a strong opening bid and are adamant that changes to entitlement programs be included in any final deal.

“It’s very much in play,” he said of the dollar-for-dollar approach. “Discretionary savings were modest but important, but really to get a handle on our finances, we’ve got to really start to save the entitlements.”

“We’ve got to start getting control of our spending,” he added. “I’d like to see us even address entitlement programs.”

In private, many in the financial industry are growing increasingly concerned about a possible default, given the broad gap between the two parties and the shrinking timeline for action.

President Obama has repeatedly said he will not negotiate over raising the debt limit even as he called congressional leaders to the White House on Wednesday to discuss both the shutdown and debt ceiling.

Some speculate stocks must crash to get the sides to compromise.

“People are willing to risk it all, the credibility of the country … for political reasons,” said one banking lobbyist. “You let the market fall by 400 or 500 points and watch the constituent calls start to come in.”

The president huddled Wednesday with the heads of the nation’s largest financial institutions, who reiterated their concern over using the debt limit as a political tool.

“Individual members of our group represent every point on the political spectrum,” Goldman Sachs head Lloyd Blankfein told reporters after the private meeting. “You can litigate these policy issues, you can re-litigate these policy issues in a public forum, but they shouldn’t use the threat of causing the U.S. to fail on its obligation to repay debt as a cudgel.”

Republicans have long argued they have public opinion on their side in the debt fight, but a new poll released Wednesday by CNN/ORC International found that a majority of the public believe failing to raise the debt limit would be a bad thing for the nation. Only 38 percent said it would be a positive.

A Quinnipiac University poll released one day earlier found 64 percent opposed blocking a debt-limit boost, while 27 percent favored it.

Those results suggest a significant shift from earlier polling, which typically found a large number of Americans opposed to hiking the borrowing limit. A Sept. 13 poll from NBC News and The Wall Street Journal found twice as many Americans opposed a debt limit boost than supported it.

Republicans insist they will have leverage in the debt-ceiling talks with the White House.

“We really need to go back and focus on the broader spending in the federal government when it comes to the debt ceiling,” Stutzman said. “I think we still have a good hand.”

But others said they were willing to consider other options as trade-offs in the talks.